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scholar. His range was probably wider than even Cayley's, for
Cayley never professed to be able to understand everything that
was going on in applied mathematics. This unique erudition
may have been a disadvantage when it came to a question of
living science as opposed to classical.
Everything that boiled up in the melting pots of physics was
grasped instantly as it appeared by Poineare and made the
topic of several purely mathematical investigations. When
wireless telegraphy was invented he seized on the new thing and
worked out its mathematics. While others were either ignoring
Einstein's early work on the (special) theory of relativity or
passing it by as a mere curiosity, Poincare was already busy
with its mathematics, and he was the first scientific man of high
standing to tell the world what had arrived and urge it to watch
Einstein as probably the most significant phenomenon of the
new era which he foresaw but could not himself usher in. It was
the same with Planck's early form of the quantum theory.
Opinions differ, of course; but at this distance it is beginning to
look as if mathematical physics did for Poincare what Ceres did
for Gauss; and although Poincare accomplished enough hi
mathematical physics to make half a dozen great reputations,
it was not the trade to which he had been born and science
would have got more out of him if he had stuck to pure mathe-
matics - his astronomical work was nothing eke. But science
got enough, and a man of Poincare's genius is entitled to his
We pass on now to the last phase of Poincaxe's universality
for which we have space: his interest in the rationale of mathe-
matical creation. In 1902 and 1904 the Swiss mathematical
periodical ISEnseignement Mathematique undertook an enquiry
into the working habits of mathematicians. Questionnaires
were issued to a number of mathematicians, of whom over a
hundred replied. The answers to the questions and an analysis
of general trends were published hi final form in 1912.* Anyone
wishing to look into the 'psychology* of mathematicians will
*Enqulte de 'ISEnseignement Zlaihematique* sur la methods de
tracail des mathtmatieiens. Available either in the periodical or in
book form (8 + 1ST pp.) from Gauthier-Yillars, Paris.